{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,16]],"date-time":"2025-11-16T05:26:25Z","timestamp":1763270785436,"version":"3.45.0"},"reference-count":34,"publisher":"MDPI AG","issue":"11","license":[{"start":{"date-parts":[[2025,11,14]],"date-time":"2025-11-14T00:00:00Z","timestamp":1763078400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100003725","name":"National Research Foundation of Korea","doi-asserted-by":"publisher","award":["2020R1G1A1A01008746"],"award-info":[{"award-number":["2020R1G1A1A01008746"]}],"id":[{"id":"10.13039\/501100003725","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100002461","name":"Chungbuk National University","doi-asserted-by":"crossref","id":[{"id":"10.13039\/501100002461","id-type":"DOI","asserted-by":"crossref"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>The index-theoretic construction of differential K-theory by Bunke and Schick uses both a geometric family and a differential form as a cocycle data. We prove that geometric families alone can codify the differential K-theory.<\/jats:p>","DOI":"10.3390\/axioms14110837","type":"journal-article","created":{"date-parts":[[2025,11,14]],"date-time":"2025-11-14T16:46:22Z","timestamp":1763138782000},"page":"837","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Geometric Families Define Differential K-Theory"],"prefix":"10.3390","volume":"14","author":[{"given":"Jae Min","family":"Lee","sequence":"first","affiliation":[{"name":"School of Mathematics and Statistics, The University of Sydney, Sydney, NSW 2006, Australia"}]},{"given":"Byungdo","family":"Park","sequence":"additional","affiliation":[{"name":"Department of Mathematics Education, Chungbuk National University, Cheongju 28644, Republic of Korea"}]}],"member":"1968","published-online":{"date-parts":[[2025,11,14]]},"reference":[{"key":"ref_1","first-page":"129","article-title":"Dirac Charge Quantization and Generalized Differential Cohomology","volume":"7","author":"Freed","year":"2000","journal-title":"J. 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